Table of Contents Author Guidelines Submit a Manuscript
Complexity
Volume 2018, Article ID 8546976, 9 pages
https://doi.org/10.1155/2018/8546976
Research Article

Extension of the Multi-TP Model Transformation to Functions with Different Numbers of Variables

Széchenyi István University, Győr, Hungary

Correspondence should be addressed to Péter Baranyi; moc.liamg@iynarab.retep.forp

Received 18 September 2017; Accepted 29 January 2018; Published 19 March 2018

Academic Editor: Kevin Wong

Copyright © 2018 Péter Baranyi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. G. W. Stewart, “On the early history of the singular value decomposition,” SIAM Review, vol. 35, no. 4, pp. 551–566, 1993. View at Publisher · View at Google Scholar · View at Scopus
  2. L. De Lathauwer, B. De Moor, and J. Vandewalle, “A multilinear singular value decomposition,” SIAM Journal on Matrix Analysis and Applications, vol. 21, no. 4, pp. 1253–1278, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. P. Baranyi, “TP model transformation as a way to LMI-based controller design,” IEEE Transactions on Industrial Electronics, vol. 51, no. 2, pp. 387–400, 2004. View at Publisher · View at Google Scholar · View at Scopus
  4. P. Baranyi, Y. Yam, and P. Varlaki, Tensor Product Model Transformation in Polytpic Model Based Control, Automation and Control Engineering, CRC Press, Taylor & Frances Grouop, March 2017.
  5. P. Baranyi, TP-Model Transformation-Based-Control Design Frameworks, Control Engineering, Springer International Publishing, Chengdo, China, 2016. View at Publisher · View at Google Scholar
  6. P. Baranyi, L. Szeidl, P. Várlaki, and Y. Yam, “Definition of the HOSVD based canonical form of polytopic dynamic models,” in Proceedings of the IEEE International Conference on Mechatronics, ICM '06, pp. 660–665, Hungary, July 2006. View at Publisher · View at Google Scholar · View at Scopus
  7. P. Baranyi, L. Szeidl, and P. Várlaki, “Numerical reconstruction of the HOSVD based canonical form of polytopic dynamic models,” in Proceedings of the 10th International Conference on Intelligent Engineering Systems '06, pp. 196–201, Agadir, Morocco, June 2006. View at Scopus
  8. P. Baranyi, “The generalized TP model transformation for T–S fuzzy model manipulation and generalized stability verification,” IEEE Transactions on Fuzzy Systems, vol. 22, no. 4, pp. 934–948, 2014. View at Publisher · View at Google Scholar · View at Scopus
  9. D. Tikk, P. Baranyi, R. Patton, and J. Tar, “Approximation capability of TP model forms,” Australian Journal of Intelligent Information Processing Systems, vol. 8, no. 3, pp. 155–163, 2004. View at Google Scholar
  10. P. Baranyi and Y. Yam, “Fuzzy Rule Base Reduction,” in Fuzzy IF-THEN Rules in Computational Intelligence: Theory and Applications, D. Ruan and and E. E. Kerre, Eds., ch. 7, pp. 135–160, Kluwer, 2000. View at Google Scholar
  11. Y. Yam, P. Baranyi, and C.-T. Yang, “Reduction of fuzzy rule base via singular value decomposition,” IEEE Transactions on Fuzzy Systems, vol. 7, no. 2, pp. 120–132, 1999. View at Publisher · View at Google Scholar · View at Scopus
  12. K. Tanaka, T. Ikeda, and H. O. Wang, “Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs,” IEEE Transactions on Fuzzy Systems, vol. 6, no. 2, pp. 250–265, 1998. View at Publisher · View at Google Scholar · View at Scopus
  13. K. Tanaka and H. Wang, “Fuzzy regulators and fuzzy observers: a linear matrix inequality approach,” in Proceedings of the 36th IEEE Conference on Decision and Control, pp. 1315–1320, San Diego, CA, USA, 2001. View at Publisher · View at Google Scholar
  14. K. Tanaka and M. Sugeno, “Stability analysis and design of fuzzy control systems,” Fuzzy Sets and Systems, vol. 45, no. 2, pp. 135–156, 1992. View at Publisher · View at Google Scholar · View at Scopus
  15. C. Scherer and S. Weiland, “Linear Matrix Inequalities in Control,” in Lecture Notes, Dutch Institute for Systems and Control, Delft, The Netherlands, 2000. View at Publisher · View at Google Scholar
  16. J. Cui, K. Zhang, and T. Ma, “An efficient algorithm for the tensor product model transformation,” International Journal of Control, Automation, and Systems, vol. 14, no. 5, pp. 1205–1212, 2016. View at Publisher · View at Google Scholar · View at Scopus
  17. S. Nagy, Z. Petres, P. Baranyi, and H. Hashimoto, “Computational relaxed TP model transformation by restriction of the computation to subspaces of the dynamic model,” in Proceedings of the ISCIII'07: 3rd International Symposium on Computational Intelligence and Intelligent Informatics, pp. 99–104, mar, March 2007. View at Publisher · View at Google Scholar · View at Scopus
  18. A. Szollosi and P. Baranyi, “Influence of the tensor product model representation of qLPV models on the feasibility of linear matrix inequality,” Asian Journal of Control, vol. 18, no. 4, pp. 1328–1342, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  19. A. Szollosi and P. Baranyi, “Improved control performance of the 3-DOF aeroelastic wing section: a TP model based 2D parametric control performance optimization,” Asian Journal of Control, vol. 19, no. 2, pp. 450–466, 2017. View at Publisher · View at Google Scholar · View at MathSciNet
  20. A. Szollosi and P. Baranyi, “Influence of the Tensor Product Model Representation of qLPV Models on the Feasibility of Linear Matrix Inequality Based Stability Analysis,” Asian Journal of Control, 2017. View at Publisher · View at Google Scholar · View at Scopus
  21. X. Liu, Y. Yu, Z. Li, H. H. C. Iu, and T. Fernando, “An Efficient Algorithm for Optimally Reshaping the TP Model Transformation,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 64, no. 10, pp. 1187–1191, 2017. View at Publisher · View at Google Scholar · View at Scopus
  22. J. Kuti, P. Galambos, and P. Baranyi, “Minimal volume simplex (MVS) polytopic model generation and manipulation methodology for TP model transformation,” Asian Journal of Control, vol. 19, no. 1, pp. 289–301, 2017. View at Publisher · View at Google Scholar · View at MathSciNet
  23. P. Várkonyi, D. Tikk, P. Korondi, and P. Baranyi, “A new algorithm for RNO-INO type Tensor Product model representation,” in Proceedings of the INES'05: IEEE 9th International Conference on Intelligent Engineering Systems, pp. 263–266, September 2005. View at Publisher · View at Google Scholar · View at Scopus
  24. X. Liu, X. Xin, Z. Li, and Z. Chen, “Near Optimal Control Based on the Tensor-Product Technique,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 64, no. 5, pp. 560–564, 2017. View at Publisher · View at Google Scholar · View at Scopus
  25. X. Liu, Y. Yu, Z. Li, H. H. C. Iu, and T. Fernando, “A novel constant gain Kalman filter design for nonlinear systems,” Signal Processing, vol. 135, pp. 158–167, 2017. View at Publisher · View at Google Scholar · View at Scopus
  26. X. Liu, Y. Yu, Z. Li, and H. H. C. Lu, “Polytopic h1 filter design and relaxation for nonlinear systems via tensor product technique,” in Signal Processing, vol. 127, pp. 191–205, 2016. View at Google Scholar
  27. P. S. Saikrishna, R. Pasumarthy, and N. P. Bhatt, “Identification and Multivariable Gain-Scheduling Control for Cloud Computing Systems,” IEEE Transactions on Control Systems Technology, vol. 25, no. 3, pp. 792–807, 2017. View at Publisher · View at Google Scholar · View at Scopus
  28. Q. Zhang and X. Zhang, Vapor Compression Cycle Control for Automotive Air Conditioning Systems with a Linear Parameter Varying Approach, Cornell University Library, 2017.
  29. G. Zhao, D. Wang, and Z. Song, “A novel tensor product model transformation-based adaptive variable universe of discourse controller,” Journal of The Franklin Institute, vol. 353, no. 17, pp. 4471–4499, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. W. Qin, B. He, Q. Qin, and G. Liu, “Robust active controller of hypersonic vehicles in the presence of actuator constraints and input delays,” in Proceedings of the 35th Chinese Control Conference, CCC 2016, pp. 10718–10723, Chengdu, China, July 2016. View at Publisher · View at Google Scholar · View at Scopus
  31. Q. Weiwei, H. Bing, L. Gang, and Z. Pengtao, “Robust model predictive tracking control of hypersonic vehicles in the presence of actuator constraints and input delays,” Journal of The Franklin Institute, vol. 353, no. 17, pp. 4351–4367, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  32. T. Wang and B. Liu, “Different polytopic decomposition for visual servoing system with LMI-based Predictive Control,” in Proceedings of the 35th Chinese Control Conference, CCC 2016, pp. 10320–10324, China, July 2016. View at Publisher · View at Google Scholar · View at Scopus
  33. T. Wang and W. Zhang, “The visual-based robust model predictive control for two-DOF video tracking system,” in Proceedings of the 28th Chinese Control and Decision Conference, CCDC 2016, pp. 3743–3747, China, May 2016. View at Publisher · View at Google Scholar · View at Scopus
  34. T. Jiang and D. Lin, “Tensor product model-based gain scheduling of a missile autopilot,” Transactions of the Japan Society for Aeronautical and Space Sciences, vol. 59, no. 3, pp. 142–149, 2016. View at Publisher · View at Google Scholar · View at Scopus
  35. A. Hajiloo, Robust and multi-objective model predictive control design for nonlinear systems [Ph.D. thesis], Concordia University, 2016.
  36. A. Hajiloo and W. F. Xie, “The stochastic robust model predictive control of shimmy vibration in aircraft landing gears,” Asian Journal of Control, vol. 17, no. 2, pp. 476–485, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  37. Y. Yu, Z. Li, J. Li, L. Li, and X. Liu, “H∞ polytopic filter design for nonlinear systems,” in Proceedings of the 35th Chinese Control Conference (CCC '16), pp. 620–625, Chengdu, China, July 2016. View at Publisher · View at Google Scholar
  38. P. Bo, Y. Lingyu, and Y. Xiaoke, “LPV-MRAC Method for Aircraft with Structural Damage,” in Proceedings of the 35th Chinese Control Conference (CCC), pp. 3262–3267, Chengdu, China, July 2016. View at Publisher · View at Google Scholar
  39. V. C. S. Campos, F. O. Souza, L. A. B. Torres, and R. M. Palhares, “New stability conditions based on piecewise fuzzy lyapunov functions and tensor product transformations,” IEEE Transactions on Fuzzy Systems, vol. 21, no. 4, pp. 748–760, 2013. View at Publisher · View at Google Scholar · View at Scopus
  40. S. Kuntanapreeda, “Tensor product model transformation based control and synchronization of a class of fractional-order chaotic systems,” Asian Journal of Control, vol. 17, no. 2, pp. 371–380, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  41. R.-E. Precup, E. M. Petriu, M.-B. Radac, S. Preitl, L.-O. Fedorovici, and C.-A. Dragos, “Cascade control system-based cost effective combination of tensor product model transformation and fuzzy control,” Asian Journal of Control, vol. 17, no. 2, pp. 381–391, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  42. G. Zhao, H. Li, and Z. Song, “Tensor product model transformation based decoupled terminal sliding mode control,” International Journal of Systems Science, vol. 47, no. 8, pp. 1791–1803, 2016. View at Google Scholar · View at MathSciNet
  43. P. Korondi, “Tensor product model transformation-based sliding surface design,” Acta Polytechnica Hungarica, vol. 3, no. 4, pp. 23–35, 2006. View at Google Scholar · View at Scopus
  44. G. Eigner, I. Böjthe, P. Pausits, and L. Kovács, “Investigation of the TP modeling possibilities of the Hovorka T1DM model,” in Proceedings of the 15th IEEE International Symposium on Applied Machine Intelligence and Informatics, SAMI 2017, pp. 259–264, Slovakia, January 2017. View at Publisher · View at Google Scholar · View at Scopus
  45. G. Eigner, P. Pausits, and L. Kovacs, “Control of T1DM via tensor product-based framework,” in Proceedings of the 17th IEEE International Symposium on Computational Intelligence and Informatics, CINTI 2016, pp. 55–60, Hungary, November 2016. View at Publisher · View at Google Scholar · View at Scopus
  46. G. Eigner, I. Rudas, A. Szakal, and L. Kovacs, “Tensor product based modeling of tumor growth,” in Proceedings of the 2017 IEEE International Conference on Systems, Man and Cybernetics (SMC), pp. 900–905, Banff, AB, October 2017. View at Publisher · View at Google Scholar
  47. L. Kovacs and G. Eigner, Usability of the tensor product based modeling in the modeling of diabetes mellitus, manuscript in preparation, 2016.
  48. G. Eigner, I. J. Rudas, and L. Kovacs, “Investigation of the TP-based modeling possibility of a nonlinear ICU diabetes model,” in Proceedings of the 2016 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2016, pp. 3405–3410, Hungary, October 2016. View at Publisher · View at Google Scholar · View at Scopus
  49. L. Kovacs and G. Eigner, “Convex polytopic modeling of diabetes mellitus: A Tensor Product based approach,” in Proceedings of the 2016 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2016, pp. 3393–3398, Hungary, October 2016. View at Publisher · View at Google Scholar · View at Scopus
  50. T. T. Wang, W. F. Xie, G. D. Liu, and Y. M. Zhao, “Quasi-min-max model predictive control for image-based visual servoing with tensor product model transformation,” Asian Journal of Control, vol. 17, no. 2, pp. 402–416, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  51. J. Kuti, P. Galambos, and Á. Miklós, “Output feedback control of a dual-excenter vibration actuator via qLPV model and TP model transformation,” Asian Journal of Control, vol. 17, no. 2, pp. 432–442, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  52. J. Pan and L. Lu, “TP model transformation via sequentially truncated higher-order singular value decomposition,” Asian Journal of Control, vol. 17, no. 2, pp. 467–475, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  53. J. Matuško, Š. Ileš, F. Kolonić, and V. Leši, “Control of 3D tower crane based on tensor product model transformation with neural friction compensation,” Asian Journal of Control, vol. 17, no. 2, pp. 443–458, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  54. V. c. Campos, L. A. Tôrres, and R. M. Palhares, “Revisiting the TP model transformation: interpolation and rule reduction,” Asian Journal of Control, vol. 17, no. 2, pp. 392–401, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  55. G. Zhao, K. Sun, and H. Li, “Tensor product model transformation based adaptive integral-sliding mode controller: Equivalent control method,” The Scientific World Journal, vol. 2013, Article ID 726963, 2013. View at Publisher · View at Google Scholar · View at Scopus
  56. S. Chumalee and J. F. Whidborne, “Gain-Scheduled H∞ Control for Tensor Product Type Polytopic Plants,” Asian Journal of Control, vol. 17, no. 2, pp. 417–431, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  57. G. Zhao, S. Huang, Y. Zhang, T. Zhang, and Y. Zhang, “Tensor product model transformation based fractional decoupled sliding-mode control for cart-pole system with time-varying sliding surfaces and Dahl friction model,” in Proceedings of the 29th Chinese Control and Decision Conference, CCDC 2017, pp. 3582–3589, China, May 2017. View at Publisher · View at Google Scholar · View at Scopus
  58. J. Klespitz, I. J. Rudas, and L. Kovacs, “LMI-Based Feedback Regulator Design via TP Transformation for Fluid Volume Control in Blood Purification Therapies,” in Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, SMC 2015, pp. 2615–2619, Hong Kong, October 2015. View at Publisher · View at Google Scholar · View at Scopus
  59. G. Zhao, C. Zhao, and D. Wang, “Tensor product model transformation based integral sliding mode control with reinforcement learning strategy,” in Proceedings of the 33rd Chinese Control Conference, CCC 2014, pp. 77–82, China, July 2014. View at Publisher · View at Google Scholar · View at Scopus
  60. S. Huang, G. Zhao, Y. Yuan, Q. Ren, and Y. Liu, “Intelligent tensor product mode transformation-based three-sliding-surface sliding mode controller design,” in Proceedings of the 34th Chinese Control Conference, CCC 2015, pp. 3258–3263, China, July 2015. View at Publisher · View at Google Scholar · View at Scopus
  61. Á. Takács, T. Haidegger, P. Galambos, J. Kuti, and I. J. Rudas, “Nonlinear soft tissue mechanics based on polytopic Tensor Product modeling,” in Proceedings of the IEEE 14th International Symposium on Applied Machine Intelligence and Informatics, SAMI '16, pp. 211–215, Slovakia, January 2016. View at Publisher · View at Google Scholar · View at Scopus
  62. B. Takarics and Y. Yam, “Robust Grid Point-Based Control Design for LPV Systems via Unified TP Transformation,” in Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, SMC '15, pp. 2626–2631, Hong Kong, October 2015. View at Publisher · View at Google Scholar · View at Scopus
  63. Z. He, M. Yin, and Y.-P. Lu, “Tensor product model-based control of morphing aircraft in transition process,” Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, vol. 230, no. 2, pp. 378–391, 2016. View at Publisher · View at Google Scholar · View at Scopus
  64. J. Chen, R. Li, and C. Cao, “Convex polytopic modeling for flexible joints industrial robot using TP-model transformation,” in Proceedings of the IEEE International Conference on Information and Automation, ICIA '14, pp. 1046–1050, Hailar, China, July 2014. View at Publisher · View at Google Scholar · View at Scopus
  65. R.-E. Precup, C.-A. Dragos, S. Preitl, M.-B. Radac, and E. M. Petriu, “Novel tensor product models for automatic transmission system control,” IEEE Systems Journal, vol. 6, no. 3, pp. 488–498, 2012. View at Publisher · View at Google Scholar · View at Scopus
  66. K. K. Wu and Y. Yam, “Control stability of TP model transformation design via probabilistic error bound of plant model,” in Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, SMC '13, pp. 1259–1264, UK, October 2013. View at Publisher · View at Google Scholar · View at Scopus
  67. R.-E. Precup, L.-T. Dioanca, E. M. Petriu, M.-B. Rǎdac, S. Preitl, and C.-A. Dragoş, “Tensor Product-based real-time control of the liquid levels in a three tank system,” in Proceedings of the 2010 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, AIM 2010, pp. 768–773, Canada, July 2010. View at Publisher · View at Google Scholar · View at Scopus
  68. K. Széll, A. Czmerk, and P. Korondi, “Automatika : časopis za automatiku, mjerenje, elektroniku, računarstvo i komunikacije,” Identifikacija modela trenja s histerezom korištenjem tenzorskog produkta, vol. 55, no. 4, pp. 463–473, 2015. View at Google Scholar
  69. F. Kolonić, A. Poljugan, and I. Petrović, “Tensor product model transformation-based controller design for gantry crane control system - An application approach,” Acta Polytechnica Hungarica, vol. 3, no. 4, pp. 95–112, 2006. View at Google Scholar · View at Scopus
  70. F. Kolonie and A. Poljugan, “Experimental control design by TP model transformation,” in Proceedings of the 2006 IEEE International Conference on Mechatronics, ICM, pp. 666–671, Hungary, July 2006. View at Publisher · View at Google Scholar · View at Scopus
  71. P. Grof and Y. Yam, “Furuta Pendulum-A Tensor Product Model-Based Design Approach Case Study,” in Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, SMC 2015, pp. 2620–2625, Hong Kong, October 2015. View at Publisher · View at Google Scholar · View at Scopus
  72. Z. Petres, Polytopic decomposition of linear parameter-varying models by tensor-product model transformation, 2006.
  73. P. Galambos, TP Model Transformation Based Control Design for Time-Delay Systems: Application in Telemanipulation, 2013.
  74. C. Ariño and A. Sala, “Relaxed LMI conditions for closed-loop fuzzy systems with tensor-product structure,” Engineering Applications of Artificial Intelligence, vol. 20, no. 8, pp. 1036–1046, 2007. View at Publisher · View at Google Scholar · View at Scopus
  75. P. Gróf, B. Takarics, Z. Petres, and P. Korondi, “Tensor product model transformation based control of a pneumatic cylinder,” in Proceedings of the 8th International Symposium on Applied Machine Intelligence and Informatics (SAMI), vol. 2008.
  76. F. Yang, Z. Chen, X. Liu, and B. Liu, “A new constant gain Kalman filter based on TP model transformation,” in Proceedings of the Chinese Intelligent Automation Conference, vol. 254, pp. 305–312, Springer, 2013. View at Scopus
  77. Š. Ileš, J. Matuško, and F. Kolonić, “Tensor product transformation based speed control of permanent magnet synchronous motor drives,” in in 17th international conference on electrical drives and power electronics, EDPE '11 (5th Joint Slovak-Croatian Conference), 2011.
  78. S. Ileš, J. Matuško, and F. Kolonić, “TP transformation based control of rotary pendulum,” in Proceedings of the 34th International Convention on Information and Communication Technology, Electronics and Microelectronics, MIPRO '11, pp. 833–839, IEEE, Opatija, Croatia, May 2011. View at Scopus
  79. R. Precup, C. Dragos, S. Preitl, M. Radac, and E. Petriu, “Tensor product models for automotive applications,” in Proceedings of the 14th International Conference on System Theory and Control (ICSTC '10), 2010.
  80. P. Korondi, “Sector sliding mode design based on tensor product model transformation,” in Proceedings of the INES 2007 - 11th International Conference on Intelligent Engineering Systems, pp. 253–258, Hungary, July 2007. View at Publisher · View at Google Scholar · View at Scopus
  81. Y. Kunii, B. Solvang, G. Sziebig, and P. Korondi, “Tensor product transformation based friction model,” in Proceedings of the INES 2007 - 11th International Conference on Intelligent Engineering Systems, pp. 259–264, Hungary, July 2007. View at Publisher · View at Google Scholar · View at Scopus
  82. P. Korondi, “Sliding sector design based on tensor product model transformation,” Transaction on Automatic Control and Computer Science, vol. 51, no. 1, pp. 101–108, 2006. View at Google Scholar
  83. P. Korondi, P. Bartal, and F. Koloni, “Friction model based on tensor product transformation,” in Proceedings of the in 7th International Symposium of Hungarian Researchers on Computational Intelligence, 2006.
  84. G. Hancke and A. Szeghegyi, “nonlinear control via tp model transformation: The tora system example,” in Proceedings of the Symposium on Applied Machine Intelligence (SAMI, '04), pp. 333–340, Herlany, Slovakia, 2004.
  85. G. Hancke and A. Szeghegyi, “Application study of the tp model transformation in the control of an inverted pendulum,” in Proceedings of the in International Conference on Computational Cybernetics (ICCC), 2003.
  86. S. Ileš, F. Kolonić, and J. Matuško, “Linear matrix inequalities based H∞ control of gantry crane using tensor product transformation,” in Proceedings of the 18th International Conference on Process Control, pp. 92–99, Tatranská Lomnica, Slovakia, 2011.
  87. A. Rövid, L. Szeidl, and P. Várlaki, “On tensor-product model based representation of neural networks,” in Proceedings of the 15th International Conference on Intelligent Engineering Systems, INES 2011, pp. 69–72, Slovakia, June 2011. View at Publisher · View at Google Scholar · View at Scopus
  88. K. Tanaka, H. Yoshida, H. Ohtake, and H. O. Wang, “A sum-of-squares approach to modeling and control of nonlinear dynamical systems with polynomial fuzzy systems,” IEEE Transactions on Fuzzy Systems, vol. 17, no. 4, pp. 911–922, 2009. View at Publisher · View at Google Scholar · View at Scopus
  89. K. Tanaka, H. Ohtake, T. Seo, M. Tanaka, and H. O. Wang, “Polynomial fuzzy observer designs: A sum-of-squares approach,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, vol. 42, no. 5, pp. 1330–1342, 2012. View at Publisher · View at Google Scholar · View at Scopus